Waiting time distribution of quantum electronic transport in the transient regime

Tang, Gaomin; Xu, Fuming; Wang, Jian

doi:10.1103/physrevb.89.205310

Cited by 56 publications

(64 citation statements)

References 42 publications

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“…While in a stationary situation the definition of the WTD requires a two-time measurement [13], in the transient case the initial time is fixed at t = 0 and one can define a single-time measurement WTD as [8,16] …”

Section: Model and Basic Theoretical Formulationmentioning

confidence: 99%

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

et al. 2015

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We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical results are obtained in the regime of very short times. We study in particular the apparent bistable behavior occurring for strong electron-phonon coupling, small bias voltages, and a detuned dot level. The results obtained are in remarkably good agreement with numerically exact results obtained by quantum Monte Carlo methods. We analyze the waiting time distribution and charge transfer probabilities, showing that only a single electron transfer is responsible for the rich structure found in the short-time regime. A universal scaling (independent of the model parameters) is found for the relative amplitude of the higher order current cumulants in the short-time regime, starting from an initially empty dot. We finally analyze the convergence to the steady state of the differential conductance and of the differential Fano factor at the inelastic threshold, which exhibits a peculiar oscillatory behavior.

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Section: Model and Basic Theoretical Formulationmentioning

confidence: 99%

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

et al. 2015

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“…[2][3][4][6][7][8][9][10][11]13,14 The question which we discuss in this paper is the following. When an electron transfers through a molecular junction, is there exists a correlation between waiting times for successive electron tunneling or they are statistically independent?…”

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confidence: 99%

“…[2][3][4][5][6][7][8][9][10][11] The statistical properties of the waiting times are usually studied using waiting time distribution (WTD), which is a conditional probability distribution that we observe the electron transfer in the detector electrode (drain or source) at time t + τ given that an electron was detected in the same electrode at time t.…”

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confidence: 99%

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

Kosov

2017

The Journal of Chemical Physics

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Quantum transport of electrons through a molecule is a series of individual electron tunneling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using master equation approach, we compute joint probability distribution for waiting times of two successive tunneling events. We show that the probability distribution is completely reset after each tunneling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunneling events become non-renewal. Non-renewal statistics between two waiting times τ1 and τ2 means that the density matrix of the molecule is not fully renewed after time τ1 and the probability of observing waiting time τ2 for the second electron transfer depends on the previous electron waiting time τ1. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in Franck-Condon blockade regime the extremely rare tunneling events become positively correlated.

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“…As discussed in details in Ref. 28 that in the transient regime, we ask how long we wait for the detection of the first transferred electron if we set t 0 = 0 as the starting point. We will use W 1 to denote the WTD in the transient regime…”

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Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach

Tang

Wang

2014

Phys. Rev. B

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We report the investigation of full-counting statistics (FCS) of transferred charge and spin in the transient regime where the connection between central scattering region (quantum dot) and leads are turned on at t = 0. A general theoretical formulation for the generating function (GF) is presented using a nonequilibrium Green's function approach for the quantum dot system. In particular, we give a detailed derivation on how to use the method of path integral together with nonequilibrium Green's function technique to obtain the GF of FCS in electron transport systems based on the two-time quantum measurement scheme. The correct long-time limit of the formalism, the Levitov-Lesovik's formula, is obtained. This formalism can be generalized to account for spin transport for the system with noncollinear spin as well as spin-orbit interaction. As an example, we have calculated the GF of spin-polarized transferred charge, transferred spin, as well as the spin transferred torque for a magnetic tunneling junction in the transient regime. The GF is compactly expressed by a functional determinant represented by Green's function and self-energy in the time domain. With this formalism, FCS in spintronics in the transient regime can be studied. We also extend this formalism to the quantum point contact system. For numerical results, we calculate the GF and various cumulants of a double quantum dot system connected by two leads in transient regime. The signature of universal oscillation of FCS is identified. On top of the global oscillation, local oscillations are found in various cumulants as a result of the Rabi oscillation. Finally, the influence of the temperature is also examined.

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Waiting time distribution of quantum electronic transport in the transient regime

Cited by 56 publications

References 42 publications

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach

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